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JohnCampbell



Joined: 16 Feb 2006
Posts: 1997
Location: Sydney

PostPosted: Mon Jun 04, 2012 2:38 am    Post subject: Reply with quote

This has been a rewarding colaborative effort as I think we are getting some useful results, thanks to David's coding efforts.
Thanks to Dan's prompting, I have now written 4 different test programs to test Dot_Product performance and the alignment impact. I would be pleased to forward these to anyone who wants them, if they provide me with email addresses, via messages.
The simplest is the MATMUL test, which I have now run using both Salford Ver 6.10 and Intel Ver 11.1 on my old Xeon processor. The performance times for 5/6 options I have tested are
Code:
Test                           Salford   Intel
MATMUL Intrinsic                 14.12    0.90
Simple 3 DO loops                10.09   10.06
2 DO + Dot_Product               10.09   10.06
Column transpose + Dot_Product    1.42    0.85
Column transpose + Vec_Sum        1.43    1.46
Column transpose + Asm_Sum        0.93   


The Intel test was compiled with /o2, which provided the SSE vector instructions.
Core i5 gave similar performance, without selecting AXV instructions.

This demonstrates that Intel's MATMUL combines the temporary transpose column and an optimised Dot_Product to achieve their performance.
For Salford, by using a temporary column and David's SSE2 assembler code, the run times are comparible to Intel's performance.

This demonstrates (in a simple example) that the performance times being achieved by other fortran compilers can be replicated with Salford by selective use of SSE2 instructions in key inner loops. From my limited experience, I have found that SSE and now AVX instructions are a relatively easy path to performance improvement, certainly easier than parallel coding approaches.

I know for my Finite Element package, there are probably only a few key loops that are critical to performance. David has now produced examples for the 2 key loops I have.
The Profile_Test example I posted on 13th May gave 6 similar DO loop coding approaches, which produced significantly different performance times with FTN95. If /opt could address some of these inefficiencies and potentially identify some SSE2 instructions for the iner loop, then FTN95 could achieve relative benchmark performance that this FTN77 achieved.

A useful result for others might be to publish and document a few simpler loop approaches, so that you might be able to utilise SSE2 instructions using FTN95.

Thanks for all the help,

John
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JohnCampbell



Joined: 16 Feb 2006
Posts: 1997
Location: Sydney

PostPosted: Fri Oct 11, 2013 2:24 am    Post subject: Reply with quote

Building on the example of Davidb, would it be possible to add some support for SSE2, SSE4 or AVX instructions in FTN95 via a math library ?
By placing this in a library, this could limit the changes required to FTN95 to making the instructions available in a CODE / EDOC block.

I have identified two main vector calculations in past posts which I would like supported and it would be good to have these available as they could significantly improve run times when used.

Code:
REAL*8 FUNCTION Dot_Product_8 ( A, B, n )
 Real*8 A(*), B(*)
 Integer*4 n

 acum = 0
 do i = 1,n
   acum = acum + A(i)*B(I)
 end do
 Dot_Product_8 = acum
END FUNCTION Dot_Product_8

REAL*8 FUNCTION Dot_Product_SSE2
REAL*8 FUNCTION Dot_Product_SSE4
REAL*8 FUNCTION Dot_Product_AVX

SUBROUTINE Vec_Add_8 ( A, B, Const, n )
 Real*8 A(*), B(*), Const
 Integer*4 n

 do i = 1,n
   A(i) = A(i) + Const * B(i)
 end do
END SUBROUTINE Vec_Add_8

SUBROUTINE Vec_Add_SSE2
SUBROUTINE Vec_Add_SSE4
SUBROUTINE Vec_Add_AVX


(I have kept the argument list as F77 style to maintain simplicity and not include the complexity of array slices or F90 interface syntax)

Is it possible to investigate this enhancement and see if it could be possible ?

Even supplying as a source code, as David has posted would provide an indication of supporting vector instructions in FTN95.
Vector instructions can be a simpler path to significant performance improvement using FTN95, without the complexity of OpenMP multi-thread.

I'm sure there are a lot of other vector or matrix calculations that could be supported, but a demonstration of the above two could be a significant start. Certainly a restricted set of MATMUL ( A x B ) or preferably ( A' x B ) as A' is a simpler calculation, based on Dot_Product.

This approach could also provide an opportunity for performance improvement while using FTN95. I would certainly like to understand the opportunities SSE4 and AVX instructions could provide for improving FTN95. Issues associated with alignment could also be investigated, although I understand newer processors have also addresed this issue with AVX. It would be good to be able to test these options !

John

I note there is even newer FMA3 instructions to support the calculation "d = a + b x c" which would suit the Vec_Add calculation. Can these be accessed via the CODE/EDOC blocks ?


Last edited by JohnCampbell on Fri Oct 11, 2013 4:43 am; edited 1 time in total
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JohnCampbell



Joined: 16 Feb 2006
Posts: 1997
Location: Sydney

PostPosted: Fri Oct 11, 2013 4:39 am    Post subject: Reply with quote

Paul,

I also note there is a compiler option /SSE2 listed from FTN95 /?.
This is not listed in FTN95.CHM.
Is this a new or obsolete option ?

John
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PaulLaidler
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Joined: 21 Feb 2005
Posts: 5585
Location: Salford, UK

PostPosted: Fri Oct 11, 2013 8:03 am    Post subject: Reply with quote

It is old and does not appear to do anything so I have now removed it from the list.
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JohnCampbell



Joined: 16 Feb 2006
Posts: 1997
Location: Sydney

PostPosted: Wed Oct 16, 2013 12:40 am    Post subject: Reply with quote

Paul,

I sent an email of an example for some of the real*8 math library, which uses the SSE routines that Davidb provided. I am not sure if they are SSE2 or SSE4 instructions.
I would like to see this library developed and either provided with FTN95 or in the coding examples.
This would provide us users of FTN95 with some access to faster computing, by way of vector instructions for a few basic types of array calculations, using CODE EDOC structures.
If it is possible to document these routines, this could provide a vehicle for enlarging the set.
My understanding of the change required to FTN95 is that more of the SSE4, AVX and possibly FMA3 instructions need to be supported by CODE/EDOC. Is this the case ?

I am at present using the 2 routines that David provided for
[a] . [b] (dot_product) and
[a] = [a] + const * [b]

There are two main areas of computing performance change that is leaving FTN95 behind, being multiple processor or larger vector registers.
My experience from testing both vector instructions and OpenMP is that vector instructions can be a much easier way of achieving 200% to 300% run time improvement, by targeting key inner loops of computation.

I'd be interested in your comments and those from others who might find this of use.

John
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PaulLaidler
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Joined: 21 Feb 2005
Posts: 5585
Location: Salford, UK

PostPosted: Wed Oct 16, 2013 7:55 am    Post subject: Reply with quote

John

Thanks for the enquiry and information.
I have logged it for investigation.

Paul
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DanRRight



Joined: 10 Mar 2008
Posts: 1878
Location: South Pole, Antarctica

PostPosted: Wed Oct 16, 2013 9:30 pm    Post subject: Reply with quote

John,
Post ***simplest possible*** benchmarks here demonstrating the effect on multiple common tasks. Dot product or matrix inversion are OK but great would be to have at least few applications like LU-factorization, Gauss or band matrix solvers for AX=B equations. In a bigger picture, after SSE support added and multithreading now working (buy 16-core latest Intel server admittedly very expensive chips and you may see tremendous speedups) this compiler will miss mostly only 64bit support
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JohnCampbell



Joined: 16 Feb 2006
Posts: 1997
Location: Sydney

PostPosted: Thu Oct 17, 2013 8:52 am    Post subject: Reply with quote

Dan,

I have written a sample program and will try to save it to dropbox.com, so that it can be downloaded.

I have run a number of tests of matrix multiplication, being:
1) using FTN95 MATMUL for C(l,n) = A(l,m) x B(m,n)
2) using vector addition using Vec_Add_SSE written by Davidb
3) using dot_product using Vec_Sum_SSE, by providing A'

The test results are in seconds
Code:

Test 1   Test 2    Test 3     Description
 20.38     2.08      1.77     uniform values of  l,m,n = 1600 1000 1400
  2.09     1.10      1.12     test with small m  l,m,n = 4500 100 3500
  3.82     1.89      1.35     test with large l  l,m,n = 12000 100 1500
 12.06     1.21      1.19     test with large m  l,m,n = 550 10000 250
  0.62     0.22      0.72     test with large n  l,m,n = 2500 10 12000

These results are with /opt compilation and show how SSE instructions can provide a significant improvement.

I'll set up the drop box from home tonight and attach the link here.

John

https://dl.dropboxusercontent.com/s/qvftgj1ezddqaqw/veclib.f90?token_hash=AAHcRRJYzeUZNOTECeJ8nVeaTOPHSULo_TAb8x3R2_1D5w&dl=1

This link appears to contain the test program I used to generate the above results.
The program consists of:
running 5 tests of matrix multiplication, multiplication, using A transpose and then using the MATMUL intrinsic.
The optimised tests are based on the 2 routines that Davidb provided.
There is also use of a timer based on CPU_clock@, which is RDTSC timer that cycles at the processor clock rate ( 2.66 ghz )

Give it a run and let me know if it works in a similar way for you.
It would be good if this could be updated to include AVX routines and could be shared with all FTN95 users who want faster real*8 vector computations.
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davidb



Joined: 17 Jul 2009
Posts: 553
Location: UK

PostPosted: Thu Oct 17, 2013 6:37 pm    Post subject: Reply with quote

It would be good if the alignment issue in FTN95 could be fixed. Then we could at least write some user contributed routines.

In the meantime, my preference has been just to use FTN95 for development, testing and debugging, and compile with gfortran (or ifort) when I want efficient release code. This is easier now that Clearwin+ is supported on other compilers (though I don't use it much personally).

This way I can take advantage of OpenMP, SSE, AVX etc.
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DanRRight



Joined: 10 Mar 2008
Posts: 1878
Location: South Pole, Antarctica

PostPosted: Tue Oct 22, 2013 2:35 am    Post subject: Reply with quote

John, davidb,

The speedups I see tell me not too much because it is not clear to me right now if SSE will be actually applied exactly to the bottlenecks of my tasks. We need more tests on general purpose cases. But it is good to ask the authors of my parallel algebra library if they use SSE and if not then ask them to try it on multiple matrix equation solvers they have in there.

Meantime want an exercise of implementing SSE on A*X = B system of linear equations solver? Here is simplest Gauss elimination program modified to solve usual square dense matrix system of equation as well as block matrix ones. The text explains it all. Play with it first (it is written intentionally a bit verbose for others if they not yet started using Clearwin+) and then try to modify the short 18 lines Gauss solver adding SSE case to the last subroutine I left empty. Run the comparison. That way we will see the difference at least on some most commonly used general purpose programs
Code:
 
!...compilation : FTN95 Bench.f95 /opt /link
   module MajorDeclarations
   use clrwin   

!.... matrix related
   real*8, dimension(:,:), allocatable :: A   
   real*8, dimension(:),   allocatable :: B, X
   integer nEquat
   integer*4, dimension(:),allocatable :: IJmax
 
!...  GUI
   real*8 ElapsedTime, Progress
   integer keySSEon   

   CONTAINS

!......................................
   integer function cbRun ()
   real*4 tStart, tFinish
   real*8 random, SEED    ! , DATE_TIME_SEED@
   integer li(100)

   CALL PERMIT_ANOTHER_callback@()

!...Allocating arrays
   allocate ( A(nEquat,nEquat), stat = li(50))
   allocate ( B(nEquat),        stat = li(51))
   allocate ( X(nEquat),        stat = li(52))
   allocate ( IJmax(nEquat),    stat = li(53))

!...Randomly fill the arrays
!  call DATE_TIME_SEED@
   SEED = 1.234
   call SET_SEED@(SEED)

   do i=1,nEquat
     B(i) = random()
     do j=1,nEquat
       A(i,j) = random()
     enddo
   enddo
   IJmax(:) = nEquat

   ElapsedTime = 0
!...Do the test
   CALL CPU_TIME(tStart)
     if(keySSEon.eq.0) then
       call GAUSS_Square_Block
     else
       call SSE_BlockSolver
     endif      
   CALL CPU_TIME(tFinish)
!...

   ElapsedTime   = tFinish - tStart
   write(*,'(a,i1, i10,a,f10.3)') 'SSE=',keySSEon, nEquat, ':', ElapsedTime
!   call window_update@(ElapsedTime)
!...Deallocating
      deallocate ( A )
      deallocate ( B )
      deallocate ( X )
      deallocate ( IJmax )
!...zeroising progress bar
      Progress = 0   
      call window_update@(Progress)

   cbRun=1
   end function   

   end module MajorDeclarations
!=================================================================
   Program Bench
   winapp
   use clrwin   
   use MajorDeclarations

   nEquat = 1000
   i=winio@('%ww%ca[A*X=B Matrix Benchmark]%1tl&', 21)
   i=winio@('Number of equations%ta%il%dd%6rd%`il%ff&',1,10000,100,nEquat)
   i=winio@('SSE Method %ta%rb[SSE]%ff %ff&',keySSEon)
   i=winio@('%cn%bc%^bt[Start]%ff %ff&', rgb@(237,177,11), cbRun)
   i=winio@('%ac[Enter]&',cbRun)   
   i=winio@('%ac[esc]&','exit')   
   i=winio@('%cn%30br%ff&', Progress, RGB@(255,0,0))
!  i=winio@('Elapsed time %ta%6rf%ff&', ElapsedTime)
   i=winio@('%30.15cw', 0)

   end   


Last edited by DanRRight on Wed Oct 23, 2013 9:26 am; edited 17 times in total
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DanRRight



Joined: 10 Mar 2008
Posts: 1878
Location: South Pole, Antarctica

PostPosted: Tue Oct 22, 2013 2:37 am    Post subject: Reply with quote

Code:
!=============================================================
!       Dan R Right 2013

   SUBROUTINE GAUSS_Square_Block
        use clrwin
        use MajorDeclarations
        real*8 FFFF, SUM
!.............................................................
!  Here IJmax is vector of lengths of rows or columns
!  For square dense matrix  IJmax(:) = nEquat
!     |--------->
!     11 12 13 14
!     21 22 23 24
!     31 32 33 34
!     41 42 43 44
!
!     Here IJmax(:) = 4
!
!  For block matrix
!     11 12 13
!     21 22 23
!     31 32 33 34 35 36
!           43 44 45 46
!           53 54 55 56
!           63 64 65 66 67 68 69
!                    76 77 78 79
!                    86 87 88 89
!                    96 97 98 99
!
!     for clarity the IJmax are plotted below together with the matrix
!
!     |------>
!     11 12 13
!     |------>
!     21 22 23
!     |--------------->
!     31 32 33 34 35 36
!     |--------------->
!           43 44 45 46
!     |--------------->
!           53 54 55 56
!     |------------------------>
!           63 64 65 66 67 68 69
!     |------------------------>
!                    76 77 78 79
!     |------------------------>
!                    86 87 88 89
!     |------------------------>
!                    96 97 98 99
!
!
!    You can see that IJmax(1:2)=3,   IJmax(3:5)=6,    IJmax(6:9)=9
!    Since blocks are of squared shape their vertical lengths are the same as horizontal ones.
!    But we will be dealing here only with the first square dense matrix case.
! ..........................................................

   DO  k=1, nEquat-1

!........ Progress
     Progress = k/(nEquat-1.)
     if(k/30*30.eq.k) then
        call temporary_yield@
        call window_update@(Progress)   
     endif
!....... End Progress

     do  I=k+1,IJmax(k)
     FFFF = A(i,k)/A(k,k)
     A(i,k)=0.
       do  j=k+1,IJmax(k)
         A(i,j) = A(i,j) - FFFF * A(k,j)
       enddo
     B(i)=B(i)-FFFF * B(k)
     enddo
   ENDDO

   X(nEquat)=B(nEquat)/A(nEquat,nEquat)
   i=nEquat-1

100   SUM=0.
      do j=i+1,IJmax(I)
        SUM = SUM + A(i,j) * X(j)
      enddo

      X(i)=(B(i)-SUM)/A(i,i)
      i=i-1
      IF(i.gt.0) GOTO 100

!     Print*,' X=',(X(i),i=1,nEquat)

10000   continue
   end subroutine
!============================================================
      subroutine SSE_BlockSolver
         print*,'SSE needs your contribution'
      end subroutine


Last edited by DanRRight on Wed Oct 23, 2013 11:47 pm; edited 2 times in total
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JohnCampbell



Joined: 16 Feb 2006
Posts: 1997
Location: Sydney

PostPosted: Wed Oct 23, 2013 5:59 am    Post subject: Reply with quote

Dan,

I have not tested the code, but basically the changes I made to your code were:
* change A to A transpose to allow sequential memory access, and
* Include the vector routines in the inner loops.

This should show the benefit of the new instructions.
Note that the 2 routines in the library are required for this solver.

John

ps: I will test the update and copy to dropbox link shortly

The change is:
Code:
   use clrwin
   use MajorDeclarations
   real*8    FFFF, SUM, Vec_Sum_SSE
   external  Vec_Sum_SSE
   integer*4 k,i, next_k

   next_k = 30
   DO  k=1, nEquat-1

!........ Progress
     if (k == next_k) then
        Progress = k/(nEquat-1.)
        call temporary_yield@
        call window_update@(Progress)   
        next_k = k+30
     endif
!....... End Progress

     do I=k+1,IJmax(k)
        FFFF = -AT(k,i)/AT(k,k)
        AT(k,i) = 0.
!          do  j=k+1,IJmax(k)
!            AT(j,i) = AT(j,i) - FFFF * AT(j,k)
!          enddo
        call Vec_Add_SSE ( AT(k+1,i), AT(k+1,k), FFFF, IJmax(k)-k)
        B(i) = B(i) + FFFF * B(k)
     end do
   END DO

!   X(nEquat) = B(nEquat)/AT(nEquat,nEquat)
! 100   SUM=0.
!      do j=i+1,IJmax(I)
!        SUM = SUM + AT(j,i) * X(j)
!      enddo
   do i = nEquat, 1, -1
      SUM  = Vec_Sum_SSE ( AT(i+1,i), X(i+1) , IJmax(I)-i )
      X(i) = (B(i)-SUM)/AT(i,i)
    end do
!      i=i-1
!      IF(i.gt.0) GOTO 100

!     Print*,' X=',(X(i),i=1,nEquat)

! 10000   continue
   end SUBROUTINE GAUSS_Square_Block
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JohnCampbell



Joined: 16 Feb 2006
Posts: 1997
Location: Sydney

PostPosted: Wed Oct 23, 2013 6:50 am    Post subject: Reply with quote

Dan,

I tested on my i5 notebook.
For 1,000 equations : gauss 4.103 seconds, SSE 0.312 seconds
For 1,500 equations : gauss 17.113 seconds, SSE 1.076 seconds
For 2,000 equations : gauss 44.819 seconds, SSE 2.574 seconds
For 3,000 equations : gauss 175.938 seconds, SSE 8.564 seconds

I would suggest that if you applied A' storage to your Gauss routine, then it would run faster, but I would still expect a saving of 2 to 4x with SSE.

I'll post the code tonight. You could add a 3rd option with A' storage.
Also you could test the solution ?

This demonstrates that there is the potential for significant performance improvement for FTN95 if these SSE ( I think SSE4 ) instructions are made available. AVX could provide a further improvement ( unless the SSE4 instructions are implemented in the AVX register on the i5 ?? )

John
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DanRRight



Joined: 10 Mar 2008
Posts: 1878
Location: South Pole, Antarctica

PostPosted: Wed Oct 23, 2013 9:14 am    Post subject: Reply with quote

Wow!
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DanRRight



Joined: 10 Mar 2008
Posts: 1878
Location: South Pole, Antarctica

PostPosted: Wed Oct 23, 2013 11:59 am    Post subject: Reply with quote

The solution looks fine, you've done good job and incredibly fast, John.
Instead of transposing block matrix case I included parallel library case. Please do the transpose case if you'll have time, my brain does not work now, 3am. Anyway, SSE is still very good, specifically for smaller matrices where parallelization takes too much overhead. Got the following timings
Code:

matrix size --> 1000    2000    3000
--------------------------------------
Dense_Block     2.22    30.4    127.
SSE             0.12    1.81    6.70
LAIPE           0.09    0.75    2.44


Parallel method though killed the timer, I do not know why. Here is the code, it will need two parallel libraries to work for all three cases.
Code:

   module MajorDeclarations
   use clrwin   

!.... matrix related
   real*8, dimension(:,:), allocatable :: A   
   real*8, dimension(:,:), allocatable :: AT   
   real*8, dimension(:),   allocatable :: B, Bsave, X
   integer nEquat
   integer*4, dimension(:),allocatable :: IJmax

!...  GUI
   real*8 ElapsedTime, Progress
   integer keyDenseBlockOn, keySSEon, keyLAIPEon   

   CONTAINS

!......................................
   integer function cbRun ()
   real*4 tStart, tFinish
   real*8 random, SEED    ! , DATE_TIME_SEED@
   integer li(100)

   CALL PERMIT_ANOTHER_callback@()

   allocate ( A(nEquat,nEquat), stat = li(50))
   allocate ( AT(nEquat,nEquat),stat = li(55))
   allocate ( B(nEquat),        stat = li(51))
   allocate ( Bsave(nEquat),    stat = li(56))
   allocate ( X(nEquat),        stat = li(52))
   allocate ( IJmax(nEquat),    stat = li(53))

!  call DATE_TIME_SEED@
   SEED = 1.234
   call SET_SEED@(SEED)

   do i=1,nEquat
     B(i) = random()
     Bsave(i) = B(i)
     do j=1,nEquat
       A(i,j) = random()
       AT(j,i) = A(i,j)
     enddo
   enddo
   IJmax(:) = nEquat

   ElapsedTime = 0
!.... Dense_Block
     if(keyDenseBlockOn.eq.1) then
       CALL CPU_TIME(tStart)
       call GAUSS_Square_Block
       CALL CPU_TIME(tFinish)
       ElapsedTime = tFinish - tStart
       write(*,'(a,i2, i10,a,f10.3)') 'DBlock=',keyDenseBlockOn, nEquat, ':', ElapsedTime
     endif

!.... SSE
     if(keySSEon.eq.1) then
       CALL CPU_TIME(tStart)
       call SSE_BlockSolver
       CALL CPU_TIME(tFinish)
       ElapsedTime = tFinish - tStart
       write(*,'(a,i2, i10,a,f10.3)') 'SSE   =',keySSEon, nEquat, ':', ElapsedTime
     endif      
   CALL CPU_TIME(tFinish)

!....  parallel
   if(keyLAIPEon.eq.1) then
     Call GetCPUs(NumberOfCPUs)
     PRINT*,' NumberOfCPUs=',NumberOfCPUs

     do nproc=1,NumberOfCPUs
       do i=1,nEquat
         do j=1,nEquat
           A(j,i) = AT(i,j)
         enddo
       enddo
       B(:) = Bsave(:)
 
     Call SetTasks(nproc)
!     CALL CPU_TIME(tStart)
          Call GetElapsedTime(tStart)
        call LAIPE_parallel_solver
          Call GetElapsedTime(tFinish)
!     CALL CPU_TIME(tFinish)
     ElapsedTime = tFinish - tStart
     write(*,'(a,i2, i10,a,f10.3)') 'N CPUs=',nproc, nEquat, ':', ElapsedTime
     enddo
   endif

      deallocate ( A )
      deallocate ( AT)
      deallocate ( B )
      deallocate ( Bsave )
      deallocate ( X )
      deallocate ( IJmax )

      Progress = 0   
      call window_update@(Progress)

   cbRun=1
   end function   

     end module MajorDeclarations


Last edited by DanRRight on Wed Oct 23, 2013 12:27 pm; edited 5 times in total
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